Analytic continuation of $\ell$-generalized Fibonacci zeta function

Dilip Kumar Sahoo; Nabin Kumar Meher

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arXiv · 2305.16184

Analytic continuation of $\ell$-generalized Fibonacci zeta function

Dilip Kumar Sahoo·Nabin Kumar Meher

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Abstract

In this paper, for any positive integer $\ell\geq2,$ we define $\ell$-generalized Fibonacci zeta function. We then study its analytic continuation to the whole complex plane $\mathbb{C}.$ Further, we compute a possible list of singularities and residues of the function at these simple poles. Moreover, we deduce that the special values of $\ell$-generalized Fibonacci zeta function at negative integer arguments are rational.

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Dilip Kumar Sahoo, Nabin Kumar Meher. 2023-05-25. Analytic continuation of $\ell$-generalized Fibonacci zeta function. https://arxiv.org/abs/2305.16184

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